Mitt Romney campaigns Wednesday in Ohio, a swing state where he is currently behind in the polls. Photograph: Alex Wong/Getty Images

Mitt Romney's campaign team insisted Wednesday the election is not slipping beyond reach in spite of a new batch of polls showing Barack Obama pulling away in the two biggest swing states, Ohio and Florida.

Victory in the two would almost certainly deliver Obama a second term in the White House.

But Ed Gillespie, one of Romney's advisers, in an interview Wednesday, challenged the accuracy of the polls, usually a sign that a campaign is in deep trouble. "It is not consistent with our polling," he said. He claimed the race is much tighter than the polls would suggest.

After months in which Obama and Romney have been tied, Obama has broken away, establishing polls leads that could prove decisive on 6 November. Polls at this stage in the race, with the electorate becoming more engaged, are often a good indicator of the eventual election result.

In Ohio, where both Obama and Romney were campaigning Wednesday, a Quinnipiac/New York Times/CBS poll put Obama on 53% to Romney on 43%. The same poll put Obama ahead too in Florida, 53% to Romney's 44%.

The Obama campaign said it is guarding against complacency. Jen Psaki, an Obama campaign spokeswoman, said: "we're running the race in every swing state as if we're five points down."

Gillespie, challenging the recent batch of polls, echoed points made by conservative bloggers who have suggested the polls are being skewed in favour of Obama. Gillespie said he was not whining but that the polls are disproportionately weighted towards the Democrats.

His basic argument is that pollsters are expecting Democrats not only to match the massive turnout in 2008 but to exceed it. "In every single one of them they have a Democratic voter participation that is higher than the Democratic voter participation in 2008," Gillespie told Fox News.

"I don't know anyone on the ground in any of these swing states that believe there will be a higher percentage of the electorate in 2012 than 2008, and yet in every single one of these surveys there's a higher percentage. Which explains, by the way, how Romney could be tied or leading among independents in these polls, and then losing the net poll to president Obama. It does not make sense."

Another of Romney's campaign team, Rich Beeson, like Gillespie, also questioned the validity of the polling. Speaking to journalists on the campaign in Ohio, he said victory for Romney was not reliant on winning Ohio and that there were other paths open.

"If we lose Ohio, can we still win? … I just don't deal in if-then statements," Beeson said. He added that no states were being written off. "So we don't sit down, I don't sit down and sort of lop those off. I prefer to look at the map holistically."

Only hours after delivering a more than competent speech at a gathering of corporate chief executives, world leaders and non-governmental-organisation heads in New York, he flew to Ohio. His effective delivery to the kind of audiences he would have been comfortable with as chief executive of Bain capital contrasted with his awkwardness in front of a Republican rally in Ohio alongside his running mate, Paul Ryan.

Video footage shows the crowd chanting "Ryan, Ryan". Romney, in an effort to work the crowd, tried to get them to chant "Romney-Ryan, Romney-Ryan". The video indicates this suggestion was met with near silence.

Romney, on completion of a two-day bus tour in Ohio, heads for another swing state, Virginia, on Thursday.